Performance Evaluation of a Lost Sales, Push-Pull, Production-Inventory System Under Supply and Demand Uncertainty
A three stages, linear, push-pull, production-inventory system is investigated. The system consists of a production station, a finished goods buffer, and a retailer following continuous review (s, Q) policy. Exponentially distributed production and transp
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Abstract A three stages, linear, push-pull, production-inventory system is investigated. The system consists of a production station, a finished goods buffer, and a retailer following continuous review (s, Q) policy. Exponentially distributed production and transportation times are assumed. External demand is modeled as a compound Poisson process, and a lost sales regime is assumed. The system is modeled as a continuous time—discreet space Markov process using Matrix Analytic methods. An algorithm is developed in MatLab to construct the transition matrix that describes the system for different parameters. The resulting system of linear equations provides the vector of the stationary probabilities, and then key performance measures such as customer service levels, average inventories etc. are computed. The proposed model can be used as a descriptive model to explore the dynamics of the system via different scenarios concerning structural characteristics. Also, it may be used as an optimization tool in the context of a prescriptive model.
1 Introduction Depending on the timing of their execution relatively to end customer demand, processes in a supply chain can be categorized as push or pull [2]. Push processes are executed in anticipation of customer orders, while in pull processes execution is initiated in response to customer demand. In usual hybrid push/pull systems production at the upstream stations is push-type, while distribution at downstream stations is controlled by pull-type policies. Such systems have been found to perform better than pure push, or pure pull systems, while they are more flexible to address growing product variety, shorter product life cycles and the need of keeping inventory costs as low as possible [4–6]. However, their analysis is more complicated. G. Varlas (B) · M. Vidalis Department of Business Administration, University of the Aegean, Michalon 8, 82100 Chios, Greece e-mail: [email protected] M. Vidalis e-mail: [email protected] © Springer International Publishing Switzerland 2017 K.F. Dœrner et al. (eds.), Operations Research Proceedings 2015, Operations Research Proceedings, DOI 10.1007/978-3-319-42902-1_62
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Cochran and Kim [3] study with Simulated Annealing a horizontally integrated hybrid production system with a movable junction point. Ghrayeb et al. [6] investigate a hybrid push/pull system of an assemble-to order manufacturing environment using discreet event simulation along with a genetic algorithm. Finally, Cuypere et al. [4] introduce a Markovian model for push-pull systems with backlogged orders, basing their analysis on quasi birth-and-death processes. The main goal of our work is to provide an algorithm for the exact evaluation of a push-pull supply network with lost sales. The resulting descriptive model can be used for the optimization of the parameters of the system.
2 Description of the System A single product, linear, push-pull supply chain is investigated (Fig. 1). A reliable and never starved station S1 produces units at
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